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[63]
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["Only the first 100 repetitions are displayed on this worksheet."]

{"sheet":"TwoVarMCSim","index":1,"n_rows":103,"n_cols":13,"rows_kept":103,"cut":false,"hidden":true,"merged":[[1,5,1,6],[3,8,3,9],[3,10,3,11],[3,12,3,13]]}
["Results of Monte Carlo Simulation"]
["Sample Number","Var1","Var2",null,null,"Simulation Stats"]
[1,null,null,null,null,null,"repetitions"]
[2,null,null,null,null,null,"secs",null,"Var1",null,"Var2",null,"Notes"]
[3,null,null,null,null,null,null,null,"Average",3.8919870765226666E-3,"Average",3.3556206172831171E-3]
[4,null,null,null,null,null,null,null,"SD",0.16598652994176216,"SD",0.14882661448398982]
[5,null,null,null,null,null,null,null,"Max",0.50081070155017959,"Max",0.40019025312581391]
[6,null,null,null,null,null,null,null,"Min",-0.54963495662729456,"Min",-0.46734164154276719]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17,null,null,null,null,1]
[18]
[19]
[20]
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["Only the first 100 repetitions are displayed on this worksheet."]

{"sheet":"Intro","index":2,"n_rows":31,"n_cols":2,"rows_kept":31,"cut":false,"hidden":false,"merged":[]}
["This workbook illustrates how within-cluster correlation in a complex survey affects OLS standard errors."]
[]
["Paper:","Barreto and Raghav, \"Understanding and Teaching Within-Cluster Correlation in Complex Surveys\""]
[]
[]
["This workbook contains Visual Basic code for four array functions:"]
["1) MULTIVARNORMAL(n, CorrRange, MeanRange, SDRange) produces an n x 1 vector of normally distributed random variables with given correlation matrix, means and SDs"]
["2) LINESTR(YRange, XRange, InterceptOption, DFOption) computes least squares estimates with robust SEs; analagous to Excel's built-in LINEST array function"]
["3) LINESTW(YRange, XRange, WeightRange, ClusterRange, StrataRange) computes least squares estimates with cluster SEs  "]
["4) OLSEXACTSE(YRange, XRange, WeightRange, ClusterRange, Rho, SigmaRange) computes exact OLS SE given rho and error dispersion"]
[null,"Rho is the within-cluster error correlation; a value from -1 to 1."]
[null,"SigmaRange is the SD of the errors in each cluster."]
[]
["You must enable macros for these functions to work."]
[]
["All four functions and matrix formulas used in this workbook are Excel array functions. "]
["Instead of Enter, array functions require input via Ctrl-Shift-Enter. Click Esc to exit an array function without making any changes."]
[]
["MULTIVARNORMAL and Monte Carlo simulation code in this workbook is from Barreto and Howland's MCSim.xla Excel add-in:"]
["http://www.wabash.edu/econometrics/EconometricsBook/Basic%20Tools/ExcelAddIns/MCSim.htm"]
["LINESTR was adapted from OLSREG function in Barreto and Howland's OLSRegression.xla Excel add-in:"]
["http://www3.wabash.edu/econometrics/EconometricsBook/Basic%20Tools/ExcelAddIns/OLSRegression.htm"]
[]
["If the functions or buttons do not work, please be sure to enable macros."]
["\"Means array\" error on open is due to a conflict with the MCSim add-in. Please uninstall the MCSim add-in when using this workbook."]
[]
["Contact Information:"]
["Humberto Barreto"]
["hbarreto@depauw.edu"]
["Manu Raghav"]
["manuraghav@depauw.edu"]

{"sheet":"DGP","index":3,"n_rows":150,"n_cols":75,"rows_kept":150,"cut":false,"hidden":false,"merged":[[32,49,32,54],[43,46,43,47],[36,62,36,65],[38,67,38,74],[8,46,8,47],[8,56,8,60],[8,62,8,65],[8,49,8,54],[8,67,8,74]]}
["This sheet uses a tiny data set to illustrate the model. It shows all calculations. Click on cells to see the formulas. Pres Esc key to get out of array function cells. "]
[]
["b0",0,null,null,null,"Red text = unobserved",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Color-coding scheme"]
["b1",2,null,null,null,"Change yellow-backgrounded cells.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Orange","Classic SE (LINEST)",null,"Press F9"]
[null,null,null,null,null,"Press F9 to recalculate the sheet. ",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Blue","Robust SE (LINESTR)"]
["n",6,"Total number of obs",null,null,"Pay attention to what bounces and what stays constant.",null,null,null,null,null,null,4,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Green","Cluster SE (LINESTW)"]
["c",3,"Number of clusters",null,null,"re",0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"OLS coefficient estimates (b) produce "]
["nc",2,"Number of obs in each cluster",null,null,"Avg e",0,{"$f":"G8","v":0},0,{"$f":"I8","v":0},0,{"$f":"K8","v":0},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Predicted Y (Y-hat) and residuals (e):"]
[null,null,null,null,null,"se",7,{"$f":"G9","v":7},7,{"$f":"I9","v":7},7,{"$f":"K9","v":7},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Classic SE",null,null,"Robust SE",null,null,null,null,null,null,"Robust SE",null,null,null,null,null,"Cluster SE",null,null,null,null,"Exact SE"]
["Intercept","X","C1","C2","C3","Cluster ID","Obs 1","Obs 2","Obs 3","Obs 4","Obs 5","Obs 6","epsilon (e)","Y",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"LINEST",null,null,"Predicted Y (Y-hat)","residuals (e)",null,null,null,null,null,null,null,null,null,null,null,null,null,"(X'X)-1",null,null,"Omega-hat",null,null,null,null,null,null,"Obs 1",null,null,null,null,null,"Cluster 1",null,null,null,null,"Cluster 1"]
[1,7.921575009337019,1,0,0,1,1,{"$f":"G7","v":0},0,0,0,0,{"$f":"multivarnormal(2,G11:H12,G8:H8,G9:H9)","v":4.6874835847873992},{"$f":"$B$3+$B$4*B11+M11","v":20.530633603461439},null,null,null,null,null,null,null,null,null,null,null,null,null,"OLS b",{"$f":"LINEST(N11:N16,B11:B16,1,1)","v":2.2923520722489492},-4.6451398701257567,null,{"$f":"$AD$11+$AC$11*B11","v":13.51389901800345},{"$f":"N11-($AD$11+$AC$11*B11)","v":7.0167345854579892},null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MINVERSE(MMULT(TRANSPOSE(A11:B16),A11:B16))","v":1.1756117747059451},-7.7670479975114948E-2,null,{"$f":"AG11^2","v":49.234564242762303},0,0,0,0,0,null,"x'e'","ex",null,"x'e'ex",null,null,"sum x'e'",null,"sum ex",null,null,"X'",null,null,"X'X",null,null,"Omega"]
[1,4.726960864091196,1,0,0,1,{"$f":"G7","v":0},1,0,0,0,0,-10.531546109266662,-1.0776243810842701,null,null,null,null,null,null,null,null,null,null,null,null,null,"Classic SE",0.5398924948369338,7.5703687516875222,null,{"$f":"$AD$11+$AC$11*B12","v":6.1907186621133796},-7.2683430431976497,null,null,null,null,null,null,null,null,null,null,null,null,null,-7.7670479975114948E-2,5.9792187022823422E-3,null,0,{"$f":"AG12^2","v":52.82881059359967},0,0,0,0,null,{"$f":"MMULT(TRANSPOSE(A11:B11),AG11)","v":7.0167345854579892},{"$f":"MMULT(AG11,A11:B11)","v":7.0167345854579892},55.583589339314756,{"$f":"MMULT(BE12:BE13,BF12:BG12)","v":49.234564242762303},390.01529370106385,null,{"$f":"BE12+BE17","v":-0.25160845773966045},null,{"$f":"BF12+BF17","v":-0.25160845773966045},{"$f":"BG12+BG17","v":21.226416227329963},null,{"$f":"TRANSPOSE(A11:B12)","v":1},1,null,{"$f":"MMULT(TRANSPOSE(A11:B12),A11:B12)","v":2},12.648535873428216,null,{"$f":"G9^2","v":49},0]
[1,14.750723446681068,0,1,0,2,0,0,1,{"$f":"G7","v":0},0,0,{"$f":"multivarnormal(2,I13:J14,I8:J8,I9:J9)","v":7.7583742607103856},37.259821154072519,null,null,null,null,null,null,null,null,null,null,null,null,null,"R2",0.81841310338336704,6.9820840226756955,"RMSE",29.168711590044754,8.0911095640277644,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,{"$f":"AG13^2","v":65.466053977101566},0,0,0,null,55.583589339314756,null,null,390.01529370106385,3089.5354038415849,null,{"$f":"BE13+BE18","v":21.226416227329963},null,null,null,null,7.921575009337019,4.726960864091196,null,12.648535873428216,85.095509639202575,null,0,{"$f":"H9^2","v":49}]
[1,12.724561789862964,0,1,0,2,0,0,{"$f":"G7","v":0},1,0,0,-2.2439461867996808,23.205177392926245,null,null,null,null,null,null,null,null,null,null,null,null,null,"F stat",18.02802115421806,4,"df",24.524035717326406,-1.3188583244001606,null,null,null,null,null,null,null,null,null,null,null,null,null,"Scroll down to see",null,null,0,0,0,{"$f":"AG14^2","v":1.7393872798395993},0,0]
[1,19.075514047177887,0,0,1,3,0,0,0,0,1,{"$f":"G7","v":0},{"$f":"multivarnormal(2,K15:L16,K8:L8,K9:L9)","v":-3.8236503769188306},34.327377717436946,null,null,null,null,null,null,null,null,null,null,null,null,null,"RSS",878.85696857654591,194.99798919881289,"SSR",39.082654285136414,-4.7552765676994682,null,null,null,null,null,null,null,null,null,null,null,null,null,"Classic SE computation",null,null,0,0,0,0,{"$f":"AG15^2","v":22.612655235311635},0,null,"Obs 2",null,null,null,null,null,"x'e'ex",null,null,null,null,"Cluster 2"]
[1,18.741095366457078,0,0,1,3,0,0,0,0,{"$f":"G7","v":0},1,-0.93150801771534186,36.550682715198811,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,38.316048929387307,-1.7653662141884965,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,0,0,0,{"$f":"AG16^2","v":3.1165178701982246},null,"x'e'","ex",null,"x'e'ex",null,null,{"$f":"MMULT(BK12:BK13,BM12:BN12)","v":6.3306816006130501E-2},-5.3407458502985943,null,null,null,"X'",null,null,"X'X",null,null,"Omega"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A12:B12),AG12)","v":-7.2683430431976497},{"$f":"MMULT(AG12,A12:B12)","v":-7.2683430431976497},-34.357173111984793,{"$f":"MMULT(BE17:BE18,BF17:BG17)","v":52.82881059359967},249.71972017243201,null,-5.3407458502985943,450.56074585585679,null,null,null,{"$f":"TRANSPOSE(A13:B14)","v":1},1,null,{"$f":"MMULT(TRANSPOSE(A13:B14),A13:B14)","v":2},27.475285236544032,null,{"$f":"I9^2","v":49},0]
["Scroll down to set Xs.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"LINESTR",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-34.357173111984793,null,null,249.71972017243201,1180.4153442468908,null,null,null,null,null,null,14.750723446681068,12.724561789862964,null,27.475285236544032,379.49831494450711,null,0,{"$f":"J9^2","v":49}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"OLS b",{"$f":"LINESTR(N10:N16,B10:B16,1,1)","v":2.2923520722489483},-4.6451398701257336,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Cluster 2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Robust SE",0.56796882570136242,8.8715634464152426,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Scroll down to see the Robust SE computation using the omega-hat matrix.",null,null,null,null,null,null,"Obs 3",null,null,null,null,null,"sum x'e' ",null,"sum ex",null,null,"Cluster 3"]
["To apply the set up above to your own example, enter the desired number of clusters and cluster size and click the Create Data button.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sample Corr of pairs of epsilons, (eci,ecj)",null,null,null,null,null,null,null,null,null,null,null,"R2",0.81841310338336681,6.9820840226756982,"RMSE",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"This shows the connection to the Classic SE which is based on an omega-hat",null,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,{"$f":"BE22+BE27","v":6.7722512396276038},null,{"$f":"BF22+BF27","v":6.7722512396276038},{"$f":"BG22+BG27","v":102.56782531486481},null,"X'",null,null,"X'X",null,null,"Omega"]
[null,null,"Number of clusters",25,25,null,null,null,null,null,null,null,null,null,null,{"$f":"M11","v":4.6874835847873992},{"$f":"M12","v":-10.531546109266662},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"matrix with RMSE2 on the diagonal, thereby collapsing to the",null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A13:B13),AG13)","v":8.0911095640277644},{"$f":"MMULT(AG13,A13:B13)","v":8.0911095640277644},119.34971955576978,{"$f":"MMULT(BE22:BE23,BF22:BG22)","v":65.466053977101566},965.67165736172035,null,{"$f":"BE23+BE28","v":102.56782531486481},null,null,null,null,{"$f":"TRANSPOSE(A15:B16)","v":1},1,null,{"$f":"MMULT(TRANSPOSE(A15:B16),A15:B16)","v":2},37.816609413634964,null,{"$f":"K9^2","v":49},0]
[null,null,"Number of obs in each cluster",4,null,null,null,null,null,null,null,null,null,null,null,-10.531546109266662,{"$f":"M11","v":4.6874835847873992},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"usual sigma-hat2 times (X'X)-1 formula.",null,null,null,null,null,null,119.34971955576978,null,null,965.67165736172035,14244.355558040896,null,null,null,null,null,null,19.075514047177887,18.741095366457078,null,37.816609413634964,715.10389169871985,null,0,{"$f":"L9^2","v":49}]
["Note: the value of rho-epsilon (the within-cluster error correlation) in cell G7 is used -- change this as needed before clicking the Create Data button.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,7.7583742607103856,{"$f":"M14","v":-2.2439461867996808},null,null,null,null,null,null,null,null,null,null,null,"LINESTW",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x'e'ex"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-2.2439461867996808,{"$f":"M13","v":7.7583742607103856},null,null,null,null,null,null,null,null,null,null,"OLS b",{"$f":"linestw(N11:N16,B11:B16,A11:A16,F11:F16)","v":2.2923520722489483},-4.6451398701257336,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"To the right is an alternative (equivalent) form of the robust SE ",null,null,null,null,null,null,"Obs 4",null,null,null,null,null,{"$f":"MMULT(BK21:BK22,BM21:BN21)","v":45.863386852637618},694.61508213450065,null,null,null,null,null,null,"re",0]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-3.8236503769188306,{"$f":"M16","v":-0.93150801771534186},null,null,null,null,null,null,null,null,null,null,"Cluster SE",0.35432438911067016,3.3722015814167565,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"via individual observations:",null,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,694.61508213450065,10520.158789820622,null,null,null,null,null,null,null,1]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-0.93150801771534186,{"$f":"M15","v":-3.8236503769188306},null,null,null,null,null,null,null,null,null,null,"R2",0.81841310338336692,6.9820840226756973,"RMSE",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A14:B14),AG14)","v":-1.3188583244001606},{"$f":"MMULT(AG14,A14:B14)","v":-1.3188583244001606},-16.781894240904975,{"$f":"MMULT(BE27:BE28,BF27:BG27)","v":1.7393872798395993},22.132940918820641]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"rho-e",{"$f":"CORREL(P22:P27,Q22:Q27)","v":-0.62466328484674805},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-16.781894240904975,null,null,22.132940918820641,281.63197431291957,null,"Cluster 3",null,null,null,null,null,null,null,"Rho for clus 1",null,null,"X'OmegaRhoX for clus 1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Exact SE",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"This representation makes it easy to compare the robust and cluster SEs.",null,null,null,null,null,null,null,null,null,null,null,null,"sum x'e' ",null,"sum ex",null,null,null,null,null,1,{"$f":"BT25","v":0},null,{"$f":"MMULT(MMULT(MMULT(BP12:BQ13,BV12:BW13),BS29:BT30),A11:B12)","v":98},619.77825779798252]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"OLSEXACTSE(N11:N16,B11:B16,A11:A16,F11:F16,0,G9:L9)","v":"SE(b1)"},"SE(b0)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Obs 5",null,null,null,null,null,{"$f":"BE32+BE37","v":-6.5206427818879646},null,{"$f":"BF32+BF37","v":-6.5206427818879646},{"$f":"BG32+BG37","v":-123.79424154219495},null,null,null,null,{"$f":"BT25","v":0},1,null,619.77825779798252,4169.679972320926]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0.5412778550909273,7.5897942633902389,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,{"$f":"BE33+BE38","v":-123.79424154219495}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Rho Value",0,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A15:B15),AG15)","v":-4.7552765676994682},{"$f":"MMULT(AG15,A15:B15)","v":-4.7552765676994682},-90.709344965367052,{"$f":"MMULT(BE32:BE33,BF32:BG32)","v":22.612655235311635},431.34802258517766,null,null,null,null,null,null,null,null,null,"Rho for clus 2",null,null,"X'OmegaRhoX for clus 2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Robust SE",null,null,null,null,null,null,-90.709344965367052,null,null,431.34802258517766,8228.1852640459601,null,"x'e'ex",null,null,null,null,null,null,null,1,{"$f":"BT25","v":0},null,{"$f":"MMULT(MMULT(MMULT(BP17:BQ18,BV17:BW18),BS33:BT34),A13:B14)","v":98},1346.2889765906575]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(BK30:BK31,BM30:BN30)","v":42.518782288987616},807.2180275514088,null,null,null,null,null,null,{"$f":"BT25","v":0},1,null,1346.2889765906575,18595.41743228085]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Obs 6",null,null,null,null,null,807.2180275514088,15325.014239007307]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,null,null,null,null,null,null,null,null,"Rho for clus 3",null,null,"X'OmegaRhoX for clus 3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A16:B16),AG16)","v":-1.7653662141884965},{"$f":"MMULT(AG16,A16:B16)","v":-1.7653662141884965},-33.084896576827902,{"$f":"MMULT(BE37:BE38,BF37:BG37)","v":3.1165178701982246},58.406958616652616,null,"Cluster SE",null,null,null,null,null,null,null,1,{"$f":"BT25","v":0},null,{"$f":"MMULT(MMULT(MMULT(BP22:BQ23,BV22:BW23),BS37:BT38),A15:B16)","v":98},1853.0138612681133]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-33.084896576827902,null,null,58.406958616652616,1094.6103814993985,null,null,null,null,null,null,null,null,null,{"$f":"BT25","v":0},1,null,1853.0138612681133,35040.090693237275]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"                                             Exact SE"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X'omega-hatX",null,null,null,null,null,null,"sum x'e'ex over all obs",null,null,null,null,null,"D = sum x'e'ex over clusters",null,null,null,null,null,null,null,null,null,null,"sum X'OmegaRhoX over clusters"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(MMULT(TRANSPOSE(A11:B16),AX11:BC16),A11:B16)","v":194.99798919881303},2117.2945933558672,null,null,"<-- Equivalent -->",null,null,{"$f":"BH12+BH17+BH22+BH27+BH32+BH37","v":194.99798919881303},{"$f":"BI12+BI17+BI22+BI27+BI32+BI37","v":2117.2945933558667},null,null,null,null,{"$f":"BK16+BK25+BK34","v":88.445475957631373},{"$f":"BL16+BL25+BL34","v":1496.4923638356108},null,null,null,null,null,null,null,null,null,{"$f":"BV29+BV33+BV37","v":294},{"$f":"BW29+BW33+BW37","v":3819.081095656753}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,2117.2945933558672,28118.733925987653,null,"X'omega-hatX = sum x'e'ex over all obs",null,null,null,{"$f":"BH13+BH18+BH23+BH28+BH33+BH38","v":2117.2945933558667},{"$f":"BI13+BI18+BI23+BI28+BI33+BI38","v":28118.733925987653},null,null,null,null,{"$f":"BK17+BK26+BK35","v":1496.4923638356108},{"$f":"BL17+BL26+BL35","v":26295.733774683787},null,null,null,null,null,null,null,null,null,{"$f":"BV30+BV34+BV38","v":3819.081095656753},{"$f":"BW30+BW34+BW38","v":57805.188097839055}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Classic SE",null,null,"(X'X)-1X'omega-hatX(X'X)-1",null,null,null,null,null,null,"(X'X)-1(sum x'e'ex)(X'X)-1",null,null,null,null,null,"(X'X)-1D(X'X)-1",null,null,null,null,null,null,null,null,null,null,"V(b) = (X'X)-1(sum X'OmegaRhoX)(X'X)-1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(MMULT($AU$11:$AV$12,AX41:AY42),$AU$11:$AV$12)","v":52.469758655847357},-3.2079359252180737,null,null,"<-- Equivalent -->",null,null,{"$f":"MMULT(MMULT($AU$11:$AV$12,BE41:BF42),$AU$11:$AV$12)","v":52.469758655847428},-3.207935925218079,null,null,null,null,{"$f":"MMULT(MMULT($AU$11:$AV$12,BK41:BL42),$AU$11:$AV$12)","v":7.5811623371396735},-0.74085697061028799,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(MMULT(AU11:AV12,BV41:BW42),AU11:AV12)","v":57.60497696059138},-3.8058535187806379]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-3.2079359252180746,0.21505905797905628,null,null,null,null,null,-3.2079359252180808,0.21505905797905672,null,null,null,null,-0.74085697061028499,8.3697181812432159E-2,null,null,null,null,null,null,null,null,null,-3.805853518780633,0.29298171641183485]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Using RMSE so df included",null,null,null,{"$f":"6/4","v":1.5},"n/(n-k) df",null,null,null,null,null,{"$f":"6/4","v":1.5},"n/(n-k) df",null,null,null,null,{"$f":"3/2","v":1.5},"c/(c-1) df",null,null,null,null,null,null,null,null,"Exact SE(b)"]
["These are the fixed Xs in the sample.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"V(b) = sigma-hat2(X'X)-1",null,null,"V(b) = (n/n-k)(X'X)-1X'omega-hatX(X'X)-1",null,null,null,"<-- Equivalent -->",null,null,"V(b) = (n/n-k)(X'X)-1(sum x'e'ex)(X'X)-1",null,null,null,null,null,"V(b) = (c/c-1)(X'X)-1D(X'X)-1",null,null,null,null,null,null,null,null,null,null,{"$f":"SQRT(BV45)","v":7.5897942633902389}]
[null,"Corr of pairs of Xs, (xci,xcj)",null,null,null,"Step X",5,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"$AD$13^2*AU11","v":57.310483036526783},{"$f":"$AD$13^2*AV11","v":-3.7863968538135193},null,{"$f":"$AY$48*AX45","v":78.704637983771036},{"$f":"$AY$48*AY45","v":-4.8119038878271105},null,null,null,null,null,{"$f":"$BF$48*BE45","v":78.704637983771136},{"$f":"$BF$48*BF45","v":-4.8119038878271185},null,null,null,null,{"$f":"$BL$48*BK45","v":11.37174350570951},{"$f":"$BL$48*BL45","v":-1.1112854559154319},null,null,null,null,null,null,null,null,null,null,{"$f":"SQRT(BW46)","v":0.5412778550909273}]
[null,{"$f":"B11","v":7.921575009337019},{"$f":"B12","v":4.726960864091196},null,"Draw Xs","rX",0.7,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"$AD$13^2*AU12","v":-3.7863968538135193},{"$f":"$AD$13^2*AV12","v":0.29148390598124807},null,{"$f":"$AY$48*AX46","v":-4.8119038878271123},{"$f":"$AY$48*AY46","v":0.32258858696858439},null,null,null,null,null,{"$f":"$BF$48*BE46","v":-4.8119038878271212},{"$f":"$BF$48*BF46","v":0.32258858696858506},null,null,null,null,{"$f":"$BL$48*BK46","v":-1.1112854559154275},{"$f":"$BL$48*BL46","v":0.12554577271864825}]
[null,4.726960864091196,{"$f":"B11","v":7.921575009337019},null,null,"Avg X",10,{"$f":"G52","v":10},{"$f":"G52+$G$50","v":15},{"$f":"I52","v":15},{"$f":"I52+$G$50","v":20},{"$f":"K52","v":20}]
[null,14.750723446681068,{"$f":"B14","v":12.724561789862964},null,null,"sX",2,{"$f":"G53","v":2},2,{"$f":"I53","v":2},2,{"$f":"K53","v":2},null,"Clicking this button pastes the Xs below as values in cells B11:B16.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"SE(b)",null,null,"SE(b)",null,null,null,null,null,null,"SE(b)",null,null,null,null,null,"SE(b)"]
[null,12.724561789862964,{"$f":"B13","v":14.750723446681068},null,null,"Cluster ID","Obs 1","Obs 2","Obs 3","Obs 4","Obs 5","Obs 6","X","The Xs below change as the sheet is recalculated (F9).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SQRT(AU50)","v":7.5703687516875151},null,null,{"$f":"SQRT(AX50)","v":8.8715634464152391},null,null,null,null,null,null,{"$f":"SQRT(BE50)","v":8.8715634464152444},null,null,null,null,null,{"$f":"SQRT(BK50)","v":3.3722015814167321}]
[null,19.075514047177887,{"$f":"B16","v":18.741095366457078},null,null,1,1,{"$f":"G51","v":0.7},{"$f":"G51","v":0.7},0,0,0,{"$f":"multivarnormal(2,G55:H56,G52:H52,G53:H53)","v":11.419918047891997},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SQRT(AV51)","v":0.53989249483693336},null,null,{"$f":"SQRT(AY51)","v":0.5679688257013622},null,null,"<-- Equivalent -->",null,null,null,{"$f":"SQRT(BF51)","v":0.56796882570136287},null,null,null,null,null,{"$f":"SQRT(BL51)","v":0.35432438911066827}]
[null,18.741095366457078,{"$f":"B15","v":19.075514047177887},null,null,1,{"$f":"G51","v":0.7},1,{"$f":"G51","v":0.7},0,0,0,11.508298228161058]
[null,"rho-X",{"$f":"CORREL(B51:B56,C51:C56)","v":0.91376336426879179},null,null,2,{"$f":"G51","v":0.7},{"$f":"G51","v":0.7},1,{"$f":"G51","v":0.7},0,0,{"$f":"multivarnormal(2,I57:J58,I52:J52,I53:J53)","v":14.398157614567962},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Classic SE using LINEST function",null,null,"ROBUST SE using LINESTR function",null,null,null,null,null,null,"ROBUST SE using LINESTR function",null,null,null,null,null,"CLUSTER SE using LINESTW function"]
[null,null,null,null,null,2,0,0,{"$f":"G51","v":0.7},1,{"$f":"G51","v":0.7},{"$f":"G51","v":0.7},15.870233066932089,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"AC12","v":0.5398924948369338},null,null,{"$f":"AC20","v":0.56796882570136242},null,null,null,null,null,null,{"$f":"AC20","v":0.56796882570136242},null,null,null,null,null,{"$f":"AC26","v":0.35432438911067016}]
["This workbook has a function that computes the",null,null,null,null,3,0,0,0,{"$f":"G51","v":0.7},1,{"$f":"G51","v":0.7},{"$f":"multivarnormal(2,K59:L60,K52:L52,K53:L53)","v":18.781744489884591}]
["intra-cluster correlation (ICC) of a variable:",null,null,null,null,3,0,0,0,{"$f":"G51","v":0.7},{"$f":"G51","v":0.7},1,17.237586093168808]
[null,"ICC",{"$f":"ICC(B11:B16,F11:F16)","v":0.9137633642687919},"Same as cell C57? Check."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"If DGP: e ~ N(0,s), r = 0",null,null,"If DGP: ei ~ N(0,si), r = 0",null,null,null,null,null,null,"If DGP: ei ~ N(0,si), r = 0",null,null,null,null,null,"If DGP: ei ~ N(0,si), r = 1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Exact SE",null,null,"Exact SE",null,null,null,null,null,null,"Exact SE",null,null,null,null,null,"Exact SE"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"SQRT(AV108)","v":0.54127785509092718},null,null,{"$f":"SQRT(AY120)","v":0.54127785509092696},null,null,"<-- Equivalent -->",null,null,null,{"$f":"SQRT(BF150)","v":0.5412778550909263},null,null,null,null,null,{"$f":"SQRT(BL150)","v":0.74879748615333719}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Assumes sigma constant",null,null,"Assumes rho = 0.",null,null,null,null,null,null,"Assumes rho = 0.",null,null,null,null,null,"Assumes rho = 1."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"and rho = 0."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"V(b) = sigma2(X'X)-1",null,null,"Sigma2",null,null,null,null,null,null,"Sigma"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"$G$9^2*AU11","v":57.604976960591308},{"$f":"$G$9^2*AV11","v":-3.8058535187806326},null,{"$f":"G9^2","v":49},0,0,0,0,0,null,{"$f":"G9","v":7}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"$G$9^2*AU12","v":-3.8058535187806326},{"$f":"$G$9^2*AV12","v":0.29298171641183479},null,0,{"$f":"H9^2","v":49},0,0,0,0,null,{"$f":"H9","v":7}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,{"$f":"I9^2","v":49},0,0,0,null,{"$f":"I9","v":7}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,0,{"$f":"J9^2","v":49},0,0,null,{"$f":"J9","v":7}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,0,0,{"$f":"K9^2","v":49},0,null,{"$f":"K9","v":7}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,0,0,0,{"$f":"L9^2","v":49},null,{"$f":"L9","v":7}]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"X'sigma2X",null,null,null,null,null,null,"Obs 1",null,null,null,null,null,"Cluster 1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(MMULT(TRANSPOSE(A11:B16),AX107:BC112),A11:B16)","v":294},3819.0810956567534,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,"sum x'e'",null,"sum ex"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3819.0810956567534,57805.188097839055,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A11:B11),BE107)","v":7},{"$f":"MMULT(BE107,A11:B11)","v":7},55.451025065359133,{"$f":"MMULT(BE116:BE117,BF116:BG116)","v":49},388.15717545751392,null,{"$f":"BE116+BE121","v":14},null,{"$f":"BF116+BF121","v":14},{"$f":"BG116+BG121","v":88.539751113997511}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,55.451025065359133,null,null,388.15717545751392,3074.8161807990869,null,{"$f":"BE117+BE122","v":88.539751113997511}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"V(b) = (X'X)-1X'sigma2X(X'X)-1"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(MMULT($AU$11:$AV$12,AX115:AY116),$AU$11:$AV$12)","v":57.604976960591245},-3.8058535187806282,null,null,null,null,null,"Obs 2",null,null,null,null,null,"x'e'ex"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,-3.8058535187806286,0.29298171641183451,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,{"$f":"MMULT(BK116:BK117,BM116:BN116)","v":196},1239.5565155959653]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,33.088726048638371,null,null,231.6210823404686,1094.8637915218394]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Cluster 2"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Obs 3",null,null,null,null,null,"sum x'e'",null,"sum ex"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,{"$f":"BE126+BE131","v":14},null,{"$f":"BF126+BF131","v":14},{"$f":"BG126+BG131","v":192.32699665580822}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A13:B13),BE109)","v":7},{"$f":"MMULT(BE109,A13:B13)","v":7},103.25506412676748,{"$f":"MMULT(BE126:BE127,BF126:BG126)","v":49},722.78544888737235,null,{"$f":"BE127+BE132","v":192.32699665580822}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,103.25506412676748,null,null,722.78544888737235,10661.608267822865]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x'e'ex"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Obs 4",null,null,null,null,null,{"$f":"MMULT(BK125:BK126,BM125:BN125)","v":196},2692.577953181315]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A14:B14),BE110)","v":7},{"$f":"MMULT(BE110,A14:B14)","v":7},89.071932529040751,{"$f":"MMULT(BE131:BE132,BF131:BG131)","v":49},623.50352770328527]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,89.071932529040751,null,null,623.50352770328527,7933.8091644579881,null,"Cluster 3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"sum x'e'",null,"sum ex"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Obs 5",null,null,null,null,null,{"$f":"BE136+BE141","v":14},null,{"$f":"BF136+BF141","v":14},{"$f":"BG136+BG141","v":264.71626589544474}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x'e'","ex",null,"x'e'ex",null,null,{"$f":"BE137+BE142","v":264.71626589544474}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"MMULT(TRANSPOSE(A15:B15),BE111)","v":7},{"$f":"MMULT(BE111,A15:B15)","v":7},133.52859833024522,{"$f":"MMULT(BE136:BE137,BF136:BG136)","v":49},934.70018831171649]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Obs 6",null,null,null,null,null,3706.0277225362261,70074.701429627792]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"x'e'","ex",null,"x'e'ex"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,131.18766756519955,null,null,918.31367295639689,17210.204121197308]
[]
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[]
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{"sheet":"Y","index":4,"n_rows":10,"n_cols":8,"rows_kept":10,"cut":false,"hidden":true,"merged":[]}
["This sheet implements the DGP with 5 clusters of 100 obs each."]
[null,null,null,null,null,null,null,"Scroll right to see results -->"]
["b0",0,"se",7]
["b1",2,"re",{"$f":"DGP!G7","v":0},"Click the Update Data button after changing re"]
[]
["n",{"$f":"B7*B8","v":100},"total number obs"]
["c",{"$f":"DGP!D22","v":25},"number of clusters"]
["nc",{"$f":"DGP!D23","v":4},"number obs in a cluster"]
[]
["X0","X1"]

{"sheet":"X","index":5,"n_rows":8,"n_cols":8,"rows_kept":8,"cut":false,"hidden":true,"merged":[]}
["This sheet controls the distribution of the Xs (average and SD) and correlation of the Xs in a cluster."]
["Step X",3,null,null,null,null,null,"Scroll right to see the results -->"]
["Avg X",10,"center of Xs"]
["SD X",2,"spread of Xs",null,null,"Click the Update X Data button after changing rx"]
["rX",0.7,"within cluster correlation of Xs"]
["n",{"$f":"Y!B6","v":100},"total number obs"]
["c",{"$f":"Y!B7","v":25},"number of clusters"]
["nc",{"$f":"Y!B8","v":4},"number obs in a cluster"]